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A304392
Numbers without a digit 1 with digits in nondecreasing order and the product of digits is a power of 6.
1
6, 23, 49, 66, 229, 236, 334, 389, 469, 666, 2233, 2269, 2349, 2366, 2899, 3338, 3346, 3689, 4499, 4669, 6666, 22239, 22336, 22499, 22669, 23334, 23389, 23469, 23666, 26899, 33368, 33449, 33466, 34899, 36689, 44699, 46669, 66666, 88999, 222299, 222333, 222369, 223349
OFFSET
1,1
COMMENTS
Applying any of the following to terms in this sequence in any order gives a term from A276038: - Prepend a 1. - Permute digits. - Do nothing.
Subsequence of A276038.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10656 (all terms with <= 23 digits)
EXAMPLE
229 is in the sequence because it has digits in nondecreasing order, no digit 1 and a product of digits 2*2*9 = 36 which is a power of 6.
MATHEMATICA
Select[Range[10^6], And[FreeQ[#, 1], AllTrue[Differences@ #, # > -1 &], IntegerQ@ Log[6, Times @@ #]] &@ IntegerDigits@ # &] (* Michael De Vlieger, Jun 30 2018 *)
PROG
(PARI) is(n) = my(d = digits(n), p = prod(i = 1, #d, d[i])); d[1] >= 2 && vecsort(d) == d && 6^logint(p, 6) == p
(Python)
from math import prod
from sympy.utilities.iterables import multiset_combinations
def auptod(maxdigs):
n, digs, alst, targets = 0, 1, [], set(6**i for i in range(1, maxdigs*3))
for digs in range(1, maxdigs+1):
mcstr = "".join(str(d)*digs for d in "234689")
for mc in multiset_combinations(mcstr, digs):
if prod(map(int, mc)) in targets: alst.append(int("".join(mc)))
return alst
print(auptod(6)) # Michael S. Branicky, Jun 23 2021
CROSSREFS
Sequence in context: A081097 A031293 A250647 * A235332 A026817 A022269
KEYWORD
nonn,base
AUTHOR
David A. Corneth, Jun 20 2018
STATUS
approved